Villian is a 45/10 but other than that I don't have any solid reads on him. Table has been fairly loose as well (typical 25NL specs.)

I checked behind on the flop because in most KK situations I think this is optimal when an ace flops (refer to Gabe's nice thread on the subject) but of course I wasn't really paying attention to the clubs.

Anyway I'm not uncomfortable with the way I played this hand; I like to keep the pot small when I don't know where I stand. However any criticisms are welcomed. Any guesses as to what Villian's possible holdings are? And what should Hero do on the river?

Thanks.

Party Poker No-Limit Hold'em, $ BB (5 handed) FTR converter on zerodivide.cx

Hero ($41.65)
Button ($18)
SB ($4.30)
BB ($27.78)
UTG ($18.35)

Preflop: Hero is MP with K, K. SB posts a blind of $0.10.
1 fold, Hero raises to $0.75, 2 folds, BB calls $0.50.

Flop: ($1.60) 4, J, A (2 players)
BB checks, Hero checks.

Turn: ($1.60) 5 (2 players)
BB checks, Hero bets $1, BB calls $1.

River: ($3.60) 2 (2 players)
BB bets $3, Hero ???